Influence of extended defects on the formation energy, hyperfine structure, and zero-field splitting of NV centers in diamond
At a Glance
Section titled “At a Glance”| Metadata | Details |
|---|---|
| Publication Date | 2021-02-15 |
| Journal | Physical review. B./Physical review. B |
| Authors | Wolfgang Körner, Daniel F. Urban, Christian Elsässer |
| Institutions | Fraunhofer Institute for Mechanics of Materials, University of Freiburg |
| Citations | 14 |
| Analysis | Full AI Review Included |
Executive Summary
Section titled “Executive Summary”This DFT study analyzes the influence of extended planar defects (Intrinsic Stacking Faults, Extrinsic Stacking Faults, and Coherent Twin Boundaries) on the properties of negatively charged Nitrogen-Vacancy (NV-) centers in diamond, providing critical data for quantum technology development.
- Energetic Preference: NV- centers are energetically preferred (segregation tendency) near all studied extended defects, with formation energy (Eform) reduced by up to 0.25 eV relative to bulk diamond.
- Short-Range Influence: The influence of the extended defects on NV- electronic and magnetic properties is strictly short-range, decaying to bulk-like behavior within approximately three double layers (~6 Å).
- ZFS Deviation: The longitudinal Zero-Field Splitting (ZFS) component (D) is reduced by up to 9% near the defects, consistent with the local appearance of hexagonal (Lonsdaleite-like) stacking sequences (ABA/BAB).
- Symmetry Breaking: Basally oriented NV- centers near defects experience C3v symmetry breaking, resulting in a non-zero transversal ZFS component (E) up to 278 MHz, which causes significant splitting of the triplet levels.
- HFS Variation: Hyperfine Structure (HFS) constants (Aii) for 14N and 13C show substantial deviations, ranging from a 10% increase/decrease (axial 14N) to a near-vanishing state (up to 90% reduction for basal 14N A33) at local hexagonal stacks.
- Engineering Relevance: These results are crucial for interpreting spectral variations in high-density NV ensembles and optimizing Chemical Vapor Deposition (CVD) growth techniques to achieve spatially localized and highly aligned NV arrays.
Technical Specifications
Section titled “Technical Specifications”| Parameter | Value | Unit | Context |
|---|---|---|---|
| Maximum Eform Reduction | -0.25 | eV | Axial NV- center located at the ISF (n=1 double layer). |
| Defect Influence Range | ~6 | Å | Distance at which NV- properties return to bulk values (approx. 3 double layers). |
| Bulk Diamond Lattice Constant (a) | 3.567 | Å | Primitive cubic cell used for DFT calculations. |
| Theoretical Bulk Axial ZFS (D0) | 3.049 | GHz | Longitudinal component D for bulk NV- (PBE functional). |
| Experimental Bulk Axial ZFS (D0) | 2.872(2) | GHz | High-precision measured value. |
| Maximum ZFS D Reduction | ~9 | % | Observed near ISF, ESF, and CTB defects. |
| Maximum Transversal ZFS (E) | 278 | MHz | Basal NV- at ISF (n=-1), due to C3v symmetry breaking. |
| 14N HFS A33 Reduction (Basal) | ~90 | % | Observed close to the defect plane (n=0 or n=1). |
| VASP Plane-Wave Cutoff Energy | 420 | eV | Used for valence electrons in DFT calculations. |
| Ionic Relaxation Force Threshold | 0.01 | eV/Å | Maximum residual force allowed during structural relaxation. |
| Thermal Energy (Room Temp) | ~0.025 | eV | 4kBT, compared to the 0.1 eV Eform difference between axial and basal NV- at ISF. |
Key Methodologies
Section titled “Key Methodologies”The study employed Density Functional Theory (DFT) using large supercell models to simulate NV- centers near extended planar defects.
- Computational Framework: Calculations were performed using the Vienna Ab Initio Simulation Package (VASP) version 5.4.4.
- Functional and Potential: The Generalized Gradient Approximation (GGA) with the Perdew, Burke, and Ernzerhof (PBE) functional was used, coupled with the Projector-Augmented-Wave (PAW) method.
- Supercell Construction:
- Bulk Reference: Hexagonal supercells (6x6x3 unit cells, 648 atoms) for cubic diamond (3C).
- Defect Models: Supercells were constructed for Intrinsic Stacking Fault (ISF, 792 atoms), Extrinsic Stacking Fault (ESF, 720 atoms), and Coherent Twin Boundary (CTB, 1152 atoms).
- Electronic Structure Parameters:
- A plane-wave cutoff energy of 420 eV was applied for valence electrons.
- Brillouin-zone integrals were evaluated using a Gamma-centered 2x2x2 k-point mesh for smaller supercells (< 800 atoms) and the Gamma-point only for larger supercells.
- Structural Relaxation: Atom positions were relaxed under constant volume conditions until the residual forces acting on atoms were less than 0.01 eV/Å.
- Property Calculation:
- Hyperfine Structure (HFS) tensor components (AIij) and Zero-Field Splitting (ZFS) tensor components (Dij) were calculated using VASP routines.
- The calculation of HFS constants relied on the PBE functional approximation, neglecting core electron contributions (AIc) due to the large supercell sizes.
Commercial Applications
Section titled “Commercial Applications”The findings directly support the engineering and optimization of diamond materials for advanced quantum and sensing technologies.
- Quantum Sensing and Metrology:
- Enables the design of highly sensitive magnetic probe arrays by exploiting the energetic preference of NV centers to localize and potentially align along extended defects created during CVD growth.
- Provides a database for interpreting complex Optically Detected Magnetic Resonance (ODMR) or Electron Paramagnetic Resonance (EPR) spectra, allowing variations in measured ZFS/HFS parameters to be traced back to specific local structural environments (e.g., ISF vs. bulk).
- Solid-State Quantum Computing:
- Aids in clarifying the interaction between the NV- electron spin (S=1) and neighboring 13C nuclear spins (I=1/2), which is critical for optimizing coherence time (T2) and developing robust solid-state qubits.
- Advanced Material Synthesis (CVD):
- Offers theoretical guidance for controlling the spatial distribution and orientation of NV centers during Chemical Vapor Deposition (CVD) processes, particularly in creating thin, highly aligned NV layers for enhanced sensor performance.
- Microstructural Defect Detection:
- Supports the use of NV ensembles as sensitive magnetic probes for detecting and characterizing microstructural defects (like dislocations or stacking faults) in electronic devices and mechanical components.
View Original Abstract
We present a density-functional theory analysis of nitrogen-vacancy (NV) centers in diamond, which are located in the vicinity of extended defects, namely, intrinsic stacking faults, extrinsic stacking faults, and coherent twin boundaries on {111} planes in diamond crystals. Several sites for NV centers close to the extended defects are energetically preferred with respect to the bulk crystal. This indicates that NV centers may be enriched at extended defects. We report the hyperfine structure and zero-field splitting parameters of the NV centers at the extended defects, which typically deviate by about 10% but in some cases up to 90% from their bulk values. Furthermore, we find that the influence of the extended defects on the NV centers is of short range: NV centers that are about three double layers (corresponding to ≈6Å) away from defect planes already show bulklike behavior.